stepson seems to hate my daughter. kinda long rant.. PLEASE HELP

i have a 6 year old step son who comes and visits every weekend. We are currently tryin to get custody of him, seein as how his mother is out on bail for murder and his grandmother doesn't take care of him. they let him do whatever he wants, whenever he wants to do it. &at our house. the rules are 100% different.

my daugher, who is turning 3, absolutely LOVES him. wants to follow him around play with him, everything. but he constantly tries to get away from her, pushes her away, hes even hit her to make her fall on the floor. which of course, pissed me off, i wanted to beat his little tail. his father doesnt see it because im the one at home with the both of them.. when he's home, his son is literally up his ass. (excuse my language, kinda irritated right now).

&i know its not just because shes 3 and annoying. he has his little cousins (slightly older and much younger than my daughter) who punch him, chase him, everything. and he plays with them with no problem. but when it comes to my daughter, he wants nothing to do with her. it is just me? does he grandmother/mother talk bad about me and my daughter? they've told him dozens of lies to try to scare him to come live with us permantely. i am six months pregnant with our son. which he does touch my belly and talks to his little brother.

but it literally makes me cry (even as im writing this), that he is so mean to my daughter. after i have my son, is he gonna start being mean to him too, because he's apart of me? WHAT CAN I DO?

I agree its not your dd that he hates.Its the idea that he is no longer number one for his father.She is a threat to his attention from his dad.Of course he is all over his dad,he is trying to get his undivided attention and love.
I would suggest you all go the therapy.